Exact mean field inference in asymmetric kinetic Ising systems

Abstract

We develop an elementary mean field approach for fully asymmetric kinetic Ising models, which can be applied to a single instance of the problem. In the case of the asymmetric SK model this method gives the exact values of the local magnetizations and the exact relation between equal-time and time-delayed correlations. It can also be used to solve efficiently the inverse problem, i.e. determine the couplings and local fields from a set of patterns, also in cases where the fields and couplings are time-dependent. This approach generalizes some recent attempts to solve this dynamical inference problem, which were valid in the limit of weak coupling. It provides the exact solution to the problem also in strongly coupled problems. This mean field inference can also be used as an efficient approximate method to infer the couplings and fields in problems which are not infinite range, for instance in diluted asymmetric spin glasses.

10 pages, 7 figures

References in corpus (10)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• The Jamming Transition in Granular Systems
• Rigorous Inequalities between Length and Time Scales in Glassy Systems
• Critical scaling in linear response of frictionless granular packings near jamming
• Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass
• Non-affine response: jammed packings versus spring networks
• Mosaic multi-state scenario vs. one-state description of supercooled liquids
• Topological persistence and dynamical heterogeneities near jamming
• Ensemble Theory for Force Networks in Hyperstatic Granular Matter
• Packing geometry and statistics of force networks in granular media

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• Origin of Corrections to Mean-field at the Onset of Unjamming
• Casimir effect between pinned particles in two-dimensional jammed systems
• Unearthing the anticrystal: criticality in the linear response of disordered solids
• Quantum kinetic theory of flux-carrying Brownian particles